Water beds are finding wider acceptance and use. However, one drawback to the acceptance and use of water beds is the difficulty of positioning, and smoothing, portions of the covers for those water beds between the sides and feet of the water-filled mattresses and the sides and feet of the confining frames of those water beds. More particularly, the contents of the water-filled mattresses of water beds continually urge the sides and feet of those mattresses against the inner surfaces of the sides and feet of the confining frames of those water beds; and a person's fingernails can be cracked or broken, and a person's fingers and hands can be abraded or scratched, during the positioning, and smoothing, of the covers between the sides and feet of those mattresses and the sides and feet of those frames.